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Scale 3539: "Aeoryllic"

Scale 3539: Aeoryllic, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

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Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Aeoryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,4,6,7,8,10,11}
Forte Number8-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2423
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 751
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsC{0,4,7}341.9
E{4,8,11}242.1
F♯{6,10,1}242.3
Minor Triadsc♯m{1,4,8}341.9
em{4,7,11}341.9
Augmented TriadsC+{0,4,8}341.9
Diminished Triadsc♯°{1,4,7}242.1
{4,7,10}242.1
{7,10,1}242.3
a♯°{10,1,4}242.1
Parsimonious Voice Leading Between Common Triads of Scale 3539. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E c#°->c#m a#° a#° c#m->a#° e°->em e°->g° em->E F# F# F#->g° F#->a#°

view full size

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3539 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3817
Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
3rd mode:
Scale 989
Scale 989: Phrolyllic, Ian Ring Music TheoryPhrolyllic
4th mode:
Scale 1271
Scale 1271: Kolyllic, Ian Ring Music TheoryKolyllic
5th mode:
Scale 2683
Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic
6th mode:
Scale 3389
Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
7th mode:
Scale 1871
Scale 1871: Aeolyllic, Ian Ring Music TheoryAeolyllic
8th mode:
Scale 2983
Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic

Prime

The prime form of this scale is Scale 751

Scale 751Scale 751, Ian Ring Music Theory

Complement

The octatonic modal family [3539, 3817, 989, 1271, 2683, 3389, 1871, 2983] (Forte: 8-Z29) is the complement of the tetratonic modal family [139, 353, 1553, 2117] (Forte: 4-Z29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3539 is 2423

Scale 2423Scale 2423, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3539 is chiral, and its enantiomorph is scale 2423

Scale 2423Scale 2423, Ian Ring Music Theory

Transformations:

T0 3539  T0I 2423
T1 2983  T1I 751
T2 1871  T2I 1502
T3 3742  T3I 3004
T4 3389  T4I 1913
T5 2683  T5I 3826
T6 1271  T6I 3557
T7 2542  T7I 3019
T8 989  T8I 1943
T9 1978  T9I 3886
T10 3956  T10I 3677
T11 3817  T11I 3259

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 3537Scale 3537: Katogian, Ian Ring Music TheoryKatogian
Scale 3541Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
Scale 3547Scale 3547: Sadygic, Ian Ring Music TheorySadygic
Scale 3523Scale 3523, Ian Ring Music Theory
Scale 3531Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri
Scale 3555Scale 3555: Pylyllic, Ian Ring Music TheoryPylyllic
Scale 3571Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
Scale 3475Scale 3475: Kylian, Ian Ring Music TheoryKylian
Scale 3507Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz
Scale 3411Scale 3411: Enigmatic, Ian Ring Music TheoryEnigmatic
Scale 3283Scale 3283: Mela Visvambhari, Ian Ring Music TheoryMela Visvambhari
Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
Scale 4051Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic
Scale 2515Scale 2515: Chromatic Hypolydian, Ian Ring Music TheoryChromatic Hypolydian
Scale 3027Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic
Scale 1491Scale 1491: Mela Namanarayani, Ian Ring Music TheoryMela Namanarayani

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.